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NEET Class neet Answered

Explain concept of current leads or lags voltage by 90
Asked by rathod1234sujal | 15 Nov, 2022, 07:10: PM
Expert Answer
Let us consider an inductor of inductance L is connected across a AC voltage source as shown in figure.
 
Let the alternating voltage v across the voltage source is
 
ξ = vm sin(ω t )......................................(1)
 
where vm is peak voltage and ω is angular frequency .
 
Voltage across inductor is given as  L (dI/dt )
 
Hence we have , L (dI/dt ) = vm sin(ωt )
 
dI = ( vm / L ) sin(ωt )
 
Current through the inductor is determined by integrating above expression
 
begin mathsize 14px style I subscript L space equals space minus space open parentheses fraction numerator v subscript m over denominator L space omega end fraction close parentheses space cos left parenthesis omega t right parenthesis space equals space space stretchy left parenthesis fraction numerator v subscript m over denominator L space omega end fraction stretchy right parenthesis space sin open parentheses omega t space minus space pi over 2 close parentheses end style  ................................(2)
where Lω is known inductive reactance
 
If we compare eqn.(1) and (2) , we see that phase of current lags by π/2 or quarter cycle
in comparision to the phase of voltage . This is illustrated in the figure given below
 
---------------------------------------------------------------------------------------------------------------
 
Let us consider now , a capacitor is connected across the alternating voltage source.
 
Voltage across capacitor  , v = q /C
 
since current is rate of flow of charge , i = dq/dt  =  C ( dv/dt )
 
Using eqn.(1) , we get ,
 
  begin mathsize 14px style i space equals space fraction numerator v subscript m over denominator 1 divided by left parenthesis C omega right parenthesis end fraction space cos left parenthesis omega t right parenthesis space equals space space fraction numerator v subscript m over denominator 1 divided by left parenthesis C omega right parenthesis end fraction space sin space left parenthesis omega t space plus space pi over 2 right parenthesis end style  ...........................(3)
where 1/(Cω) is capacitive reactance .
 
if we compare eqn.(1) and eqn.(3) , we see that phase of current leads by π/2 or one quarter of cycle .
 
This is illustrated in the figure given below
 

 




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